Another approach to this problem would be to avoid perl's limitation in conversion of the number between string and float.

This C code:

int main(void)
{
  double d;
  d=1.0;
  while(d>0.0)
  {
    printf("%100.80e\n",d);
    d = d/2.0;
  }
  return 1;
}
[download]

produces the exact same result as this perl code:

  my $d;
  $d=1.0;
  while($d>0.0)
  {
    printf("%100.80e\n",$d);
    $d = $d/2.0;
  }
[download]

But this is completely different from this perl code, which includes a conversion to string:

  my $d;
  $d=1.0;
  while($d>0.0)
  {
    $d= "$d";
    printf("%100.80e\n",$d);
    $d = $d/2.0;
  }
[download]

The output from the perl program with the string conversion is clearly messed up; it prints these two successive values:

2.38418579101562500000000000000000000000000000000000000000000000000000
+000000000000e-07
1.19209289550780998537093783879586839091757610731292515993118286132812
+500000000000e-07
[download]

Where the C code and perl code without the string conversion has the correct result:

2.38418579101562500000000000000000000000000000000000000000000000000000
+000000000000e-07
1.19209289550781250000000000000000000000000000000000000000000000000000
+000000000000e-07
[download]

It would be nice if there were a way to tell perl "don't ever convert this number to a string unless I say it's okay." Short of that, you have to either be careful to avoid string conversion, write your numerical code in XS, use BigFloat a lot, or use straight C or FORTRAN. The Inline module also makes calling C easy. C is almost as easy as perl for numerical programming anyway. The PDL module may also do a better job for what you need, especially if you can formulate your problem in terms of vectors or matrices. That way you would gain in both speed and precision!

It should work perfectly the first time! - toma